Solve sqrt{1-(6/7)^2}

$$\sqrt { 1 - ( \frac { 6 } { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{13}}{7}\approx 0.515078754$$

Solution Steps

Calculate \frac{6}{7} to the power of 2 and get \frac{36}{49}.

$$\sqrt{1-\frac{36}{49}}$$

Convert 1 to fraction \frac{49}{49}.

$$\sqrt{\frac{49}{49}-\frac{36}{49}}$$

Since \frac{49}{49} and \frac{36}{49} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{49-36}{49}}$$

Subtract 36 from 49 to get 13.

$$\sqrt{\frac{13}{49}}$$

Rewrite the square root of the division \sqrt{\frac{13}{49}} as the division of square roots \frac{\sqrt{13}}{\sqrt{49}}.

$$\frac{\sqrt{13}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{\sqrt{13}}{7}$$